Find angle A if it is greater than or equal to 0 degrees and smaller than or equal to 180 degrees. round to the nearest tenth of a degree, if necessary.
a) sinA = 0.5
b) cosA = -0.5
e) cosA = 0.4561
g) sinA = 0.5736
PLEASE HELP WID THIS!!:( i tried so much! but im not getting it...
Thanks I greatly appreciate it sooo much!!:)
If sin A = 0.5, doesn't that make A =- 30 degrees. That is >0 and <180 so it qualifies. Just punch in the other numbers on your calculator and read the angle A. See if it meets the criteria.
Thanks
That - slipped in. Sin A = 0.5; A = 30 degrees and not -30 degrees.
To find the value of angle A for each of the given trigonometric functions, you can use inverse trigonometric functions. Here's how you can solve for each option:
a) sinA = 0.5
To find the value of angle A, you can use the inverse sine function (or arcsine). Take the inverse sine of 0.5:
A = sin^(-1)(0.5) [sin^(-1) is the inverse sine function]
Using a calculator or a table of values, you would find that sin^(-1)(0.5) is approximately 30 degrees. So, angle A is 30 degrees.
b) cosA = -0.5
Similarly, to find the value of angle A, you can use the inverse cosine function (or arccosine). Take the inverse cosine of -0.5:
A = cos^(-1)(-0.5) [cos^(-1) is the inverse cosine function]
Using a calculator or a table of values, you would find that cos^(-1)(-0.5) is approximately 120 degrees (or 240 degrees if you consider negative angles in the counterclockwise direction). So, angle A can be either 120 degrees or 240 degrees.
e) cosA = 0.4561
To find the value of angle A, you can again use the inverse cosine function. Take the inverse cosine of 0.4561:
A = cos^(-1)(0.4561) [cos^(-1) is the inverse cosine function]
Using a calculator or a table of values, you would find that cos^(-1)(0.4561) is approximately 63.389 degrees. So, angle A is approximately 63.4 degrees.
g) sinA = 0.5736
Lastly, to find the value of angle A, you can use the inverse sine function. Take the inverse sine of 0.5736:
A = sin^(-1)(0.5736) [sin^(-1) is the inverse sine function]
Using a calculator or a table of values, you would find that sin^(-1)(0.5736) is approximately 34.952 degrees. So, angle A is approximately 35.0 degrees.
Note that these values are rounded to the nearest tenth of a degree as requested.
If you're using a scientific calculator, remember to set it to the appropriate angle unit (degrees or radians) before performing the inverse trigonometric functions.